{
  "abstract": "We introduce the left and right Cayley graphs of a finite skew brace $(A,\\cdot, \\circ)$ with a connection set $T\\subset A$, as a directed multigraph with additive and multiplicative edges, depicting the operations $\\cdot$ and $\\circ$ respectively. We compute the distance from $a$ to $a\\circ b$ in these Cayley graphs in terms of factorization lengths over $T$. As an application, we provide a characterization of the ideals of a skew brace in terms of their corresponding Cayley graphs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.35388",
  "author_total": 3,
  "authors": [
    {
      "name": "Ahmad Syarif Ahdal"
    },
    {
      "name": "Ryan Aziz"
    },
    {
      "name": "Denny Riama Silaban"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bnfsvnhe33y5q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35388",
  "fulltext_url": null,
  "id": "bnfsvnhe33y5q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.35388",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.GR"
    ],
    [
      "openalex",
      "2602|Rings, Modules, and Algebras"
    ]
  ],
  "openalex": "W7224000683",
  "pdf_url": "https://arxiv.org/pdf/2610.35388",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bnfsvnhe33y5q.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.35388",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35388"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "On Cayley Graphs of Skew Braces and Their Distances",
  "title_text": "On Cayley Graphs of Skew Braces and Their Distances",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/bnfsvnhe33y5q",
  "venue": "arXiv",
  "versions": []
}